{"schema":"vela.problem-packet.v0.1","problem":782,"statement":"Do the squares contain arbitrarily long quasi-progressions? That is, does there exist some constant $C>0$ such that, for any $k$, the squares contain a sequence $x_1,\\ldots,x_k$ where, for some $d$ and all $1\\leq i<k$,\\[x_i+d\\leq x_{i+1}\\leq x_i+d+C.\\]Do the squares contain arbitrarily large cubes\\[a+\\left\\{ \\sum_i \\epsilon_ib_i : \\epsilon_i\\in \\{0,1\\}\\right\\}?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}